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Approximate factor models with weaker loadings

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  • Bai, Jushan
  • Ng, Serena

Abstract

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where Λ0′Λ0/Nα is positive definite in the limit when α=1, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when α∈(0,1] albeit at slower rates and under additional assumptions on the sample size. The results hold whether α is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.

Suggested Citation

  • Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1893-1916
    DOI: 10.1016/j.jeconom.2023.01.027
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    Cited by:

    1. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org.
    2. Jungjun Choi & Ming Yuan, 2024. "High Dimensional Factor Analysis with Weak Factors," Papers 2402.05789, arXiv.org.
    3. Jad Beyhum, 2024. "Counterfactuals in factor models," Papers 2401.03293, arXiv.org.
    4. Lihua Lei & Brad Ross, 2023. "Estimating Counterfactual Matrix Means with Short Panel Data," Papers 2312.07520, arXiv.org.
    5. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Models without Estimating the Rank," Papers 2311.16440, arXiv.org.

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    More about this item

    Keywords

    Principal components; Low rank decomposition; Weak factors; Factor augmented regressions;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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